XT-Hypergraph-Based Decomposition and Implementation of Concurrent Control Systems Modeled by Petri Nets

This paper presents an integrated approach to the structural decomposition of concurrent control systems using exact transversal hypergraphs (XT-hypergraphs). The proposed method combines formal properties of XT-hypergraphs with invariant-based Petri net analysis to enable automatic partitioning of complex, concurrent specifications into deterministic and independent components. The approach focuses on preserving behavioral correctness while minimizing inter-component dependencies and computational complexity. By exploiting the uniqueness of minimal transversal covers, reducibility, and structural stability of XT-hypergraphs, the method achieves a deterministic decomposition process with polynomial-delay generation of exact transversals. The research provides practical insights into the construction, reduction, and classification of XT structures, together with quality metrics evaluating decomposition efficiency and structural compactness. The developed methodology is validated on representative real-world control and embedded systems, showing its applicability in deterministic modeling, analysis, and implementation of concurrent architectures. Future work includes the integration of XT-hypergraph algorithms with adaptive decomposition and verification frameworks to enhance scalability and automation in modern system design and integration with currently popular AI and machine learning methods.